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Research & Reviews : Journal of Statistics

Bayesian Analysis of Operating Characteristic Curves of Single Sampling Plans by Attributes under Mixture of Two Binomial Distributions

  1. M. Saral
  2. A. Loganathan
  3. P. Muthu Krishnan
  4. R. Vijaya Raghavan

Abstract

In the current scenario, manufacturing of products in single stream is not enough to meet the needs of consumers and in order to increase the production, two or more streams are required and the lots are formed from various streams. The production unit differs due to input raw materials, machineries, manpower and management, there may be inherent variation among the quality of the products manufactured from different streams. In this situation, the simple probability distribution is not appropriate and instead, finite mixture distribution is more appropriate. A finite mixture distribution is an appropriate probability distribution to study the product quality of such heterogeneous lots. In this paper, the operating characteristic (OC) function for Bayesian single sampling plans by attributes under the conditions of mixture of two binomial distributions is derived. The OC curves are drawn for different sets of parameters. Properties of the OC function with reference to the plan parameters are studied from the empirical analysis of the behaviour of the OC curves. Keywords: Single sampling plan, mixture of two binomial distributions, operating characteristic function, producer quality level, consumer quality level, producer’s risk, consumer’s risk, prior distributionCite this ArticleSaral M, Loganathan A, Muthu Krishnan P, et al. Bayesian Analysis of Operating Characteristic Curves of Single Sampling Plans by Attributes under Mixture of Two Binomial Distributions. Research & Reviews: Journal of Statistics. 2018; 7(1): 12s–23sp.

References (17)

  1. Schilling EG, Neubauer DV. Acceptance Sampling in Quality Control. 2nd Edn. Boca Raton: CRC Press; 2009.
  2. Stephens KS. The Handbook of App lied Acceptance Sampling Plans, Procedures and Principles . Milwaukeee, Wisconsin: ASQ Quality Press; 2001.
  3. Calvin TW. How and When to Perform Bayesian Acceptance Sampling . Vol. 7. Wisconsin: American Society for Quality Control; 1990.
  4. Hald A. Statistical T heory of Sampling Inspection by Attributes . New York: Academic Press; 1981.
  5. Weiler H. The Use of Incomplete Beta Functions for Prior Distributions in Binomial Sampling. Technometrics. 1965; 7(3): 335–47p.
  6. Rajagopal K, Loganathan A, Vijayaraghavan R. An Empirical Study of Operating Characteristic Curves of Beta - Binomial Sampling Plans. Senthamarai Kannan K, et al., editors. Contributions to Statistical Research . India: Publications Division, Manonmaniam Sundaranar University; 2005; 111–27p.
  7. Vijayaraghavan R , Loganathan A, Rajagopal K. Analysis of Operating Characteristic Curves of Gamma -Poisson Sampling Plans. Amer J Math Management Sci . 2007; 27(1&2): 163– 77p.
  8. Loganathan A, Rajagopal K, Vijayaraghavan R. A Study on the Behaviour of Operating Characteristic Curves of Sampling Plans Based on Polya Distribution. Am J Math Management Sci . 2007; 27(1&2): 111–22p.
  9. Loganathan A, Saral M, Vijayaraghavan R, et al . Analysis of the Operating Characteristic Curves of Bayesian Single Sampling Plan by Attributes for Non - Homogeneous Lots. In: Senthamarai Kannan K, Loganathan A, editors. New Methodologies in Statistical Research . India: Publication Division, Manonmaniam Sundaranar University ; 2012; 47–52p.
  10. Mussida A, Barron UG, Butler F. Operating Characteristic Curves for Single, Double and Multiple Fraction Defective Sampling Plans Developed for Cronobacter in Powder Infant Formula. Procedia Food Sci. 2011; 1: 979–86p.
  11. Everitt BS, Hand DJ. Finite Mixture Distributions. London: Chapman and Hall; 1981.
  12. Titterington DM, Smith AFM, Makov UE. Statistical Analysis of Finite Mixture Distributions. New York: Wiley; 1985.
  13. McLachlan G, Peel D. Finite Mixture Models. New York: Wiley; 2000. Bayesian Analysis of OC Curves of SSP Saral et al. RRJoST (2018) 12s-23s © STM Journals 2018. All Rights Reserved Page 23s
  14. Quinino RC, Ho LL, Suyama E. Alternative Estimator for the Parameters of a Mixture of Two Binom ial Distributions. Stat Papers . 2013; 54: 47– 69p.
  15. Abdelwahab S, Alshammari T. Parameter Estimation of Mixture of Two Binomial Distributions. Estimation, Filtering and Detection, Project Report No. ECE 565, Oregon State University; 2013.
  16. Loganathan A, Muthu Krishnan P, Saral M, et al . Empirical Analysis of the OC Function of SSPs under the Conditions of a Mixture of Two Poisson Distributions. In: Senthamarai Kannan K, Loganathan A, editors. Recent Trends in Statistics and Computer Applications. India: Publication Division, Manonmaniam Sundaranar University; 2011; 77–82p.
  17. Loganathan A, Muthu Krishnan P, Vijayaraghavan R, et al . Evaluation of Single Sampling Plans by Attributes Using Mixture of Two Distributions. J Test Eval. 2013; 41(4): 675–684p. Cite this Article Saral M, Loganat han A, Muthu Krishnan P, et al. Bayesian Analysis of Operating Characteristic Curves of Single Sampling Plans by Attributes under Mixture of Two Binomial Distributions . Research & Reviews: Journal of Statistics . 2018; 7(1): 12s–23sp.
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